The BSE-30 share index Sensex opened higher at 20,944.14 and moved up further to cross the 21,000 level to 21,037.59 points on strong buying.
But it declined marginally afterwards to 20,937.12 before bouncing back to quote at 21,007.41 points in mid-morning trade.
The NSE 50-share barometer Nifty also looked up further by 16.45 points, or 0.26 per cent, to 6,237.35 at 1030 hours.
Foreign institutional investors (FIIs) continued their buying spree as they invested a net Rs 1103.04 crores yesterday, as per provisional data from the stock exchanges.
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The market may remain volatile ahead of the expiry of October contract tomorrow.
Asian stocks rose in their early trade amid rising company earnings and with the Federal Reserve projected to maintain the pace of its monetary stimulus today.
Key benchmark indices in China, Japan, Hong Kong, Taiwan, Singapore and South Korea rose 0.06 to 1.22 per cent.